Question: Simplify the following expression: $r = \dfrac{10a^2 - 30a - 700}{a - 10} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $10$ , so we can rewrite the expression: $ r =\dfrac{10(a^2 - 3a - 70)}{a - 10} $ Then we factor the remaining polynomial: $a^2 {-3}a {-70} $ ${-10} + {7} = {-3}$ ${-10} \times {7} = {-70}$ $ (a {-10}) (a + {7}) $ This gives us a factored expression: $\dfrac{10(a {-10}) (a + {7})}{a - 10}$ We can divide the numerator and denominator by $(a + 10)$ on condition that $a \neq 10$ Therefore $r = 10(a + 7); a \neq 10$